Solve for $x$ : $x^2 + 5x - 24 = 0$
Answer: The coefficient on the $x$ term is $5$ and the constant term is $-24$ , so we need to find two numbers that add up to $5$ and multiply to $-24$ The two numbers $-3$ and $8$ satisfy both conditions: $ {-3} + {8} = {5} $ $ {-3} \times {8} = {-24} $ $(x {-3}) (x + {8}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -3) (x + 8) = 0$ $x - 3 = 0$ or $x + 8 = 0$ Thus, $x = 3$ and $x = -8$ are the solutions.